DOCSLIB.ORG

High Performance Computing ADVANCED SCIENTIFIC COMPUTING

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
High Performance Computing ADVANCED SCIENTIFIC COMPUTING High Performance Computing ADVANCED SCIENTIFIC COMPUTING Prof. Dr. – Ing. Morris Riedel Adjunct Associated Professor School of Engineering and Natural Sciences, University of Iceland, Reykjavik, Iceland Research Group Leader, Juelich Supercomputing Centre, Forschungszentrum Juelich, Germany @MorrisRiedel LECTURE 1 @Morris Riedel @MorrisRiedel High Performance Computing September 5, 2019 Room V02-258 Review of Practical Lecture 0.2 – Short Intro to C Programming & Scheduling . Many C/C++ Programs used in HPC today . Multi-user HPC usage needs Scheduling Many multi-physics application challenges [3] LLview on different scales & levels of granularity drive the need for HPC [1] Terrestrial Systems SimLab [2] NEST Web page not good! right way! Lecture 1 – High Performance Computing 2/ 50 Outline of the Course 1. High Performance Computing 11. Scientific Visualization & Scalable Infrastructures 2. Parallel Programming with MPI 12. Terrestrial Systems & Climate 13. Systems Biology & Bioinformatics 3. Parallelization Fundamentals 14. Molecular Systems & Libraries 4. Advanced MPI Techniques 15. Computational Fluid Dynamics & Finite Elements 5. Parallel Algorithms & Data Structures 16. Epilogue 6. Parallel Programming with OpenMP 7. Graphical Processing Units (GPUs) + additional practical lectures & Webinars for our hands-on assignments in context 8. Parallel & Scalable Machine & Deep Learning 9. Debugging & Profiling & Performance Toolsets . Practical Topics 10. Hybrid Programming & Patterns . Theoretical / Conceptual Topics Lecture 1 – High Performance Computing 3/ 50 Outline . High Performance Computing (HPC) Basics . Four basic building blocks of HPC . TOP500 & Performance Benchmarks . Multi-core CPU Processors . Shared Memory & Distributed Memory Architectures . Hybrid Architectures & Programming . HPC Ecosystem Technologies . HPC System Software Environment – Revisited . System Architectures & Network Topologies . Many-core GPUs & Supercomputing Co-Design . Relationships to Big Data & Machine/Deep Learning . Data Access & Large-scale Infrastructures Lecture 1 – High Performance Computing 4/ 50 Selected Learning Outcomes . Students understand… . Latest developments in parallel processing & high performance computing (HPC) . How to create and use high-performance clusters . What are scalable networks & data-intensive workloads . The importance of domain decomposition . Complex aspects of parallel programming . HPC environment tools that support programming or analyze behaviour . Different abstractions of parallel computing on various levels . Foundations and approaches of scientific domain- specific applications . Students are able to … . Programm and use HPC programming paradigms . Take advantage of innovative scientific computing simulations & technology . Work with technologies and tools to handle parallelism complexity Lecture 1 – High Performance Computing 5/ 50 High Performance Computing (HPC) Basics Lecture 1 – High Performance Computing 6/ 50 What is High Performance Computing? . Wikipedia: ‘redirects from HPC to Supercomputer’ . Interesting – gives us already a hint what it is generally about . A supercomputer is a computer at the frontline of contemporary processing capacity – particularly speed of calculation [4] Wikipedia ‘Supercomputer’ Online . HPC includes work on ‘four basic building blocks’ in this course . Theory (numerical laws, physical models, speed-up performance, etc.) . Technology (multi-core, supercomputers, networks, storages, etc.) . Architecture (shared-memory, distributed-memory, interconnects, etc.) . Software (libraries, schedulers, monitoring, applications, etc.) [5] Introduction to High Performance Computing for Scientists and Engineers Lecture 1 – High Performance Computing 7/ 50 Understanding High Performance Computing (HPC) – Revisited . High Performance Computing (HPC) is based on computing resources that enable the efficient use of parallel computing techniques through specific support with dedicated hardware such as high performance cpu/core interconnections. HPC network interconnection important . High Throughput Computing (HTC) is based on commonly available computing resources such as commodity PCs and small clusters that enable the execution of ‘farming jobs’ without providing a high performance interconnection between the cpu/cores. network interconnection HTC less important! The complementary Cloud Computing & Big Data – Parallel Machine & Deep Learning Course focusses on High Throughput Computing Lecture 1 – High Performance Computing 8/ 50 Parallel Computing . All modern supercomputers depend heavily on parallelism . Parallelism can be achieved with many different approaches . We speak of parallel computing whenever a number of ‘compute elements’ (e.g. cores) solve a problem in a cooperative way [5] Introduction to High Performance Computing for Scientists and Engineers . Often known as ‘parallel processing’ of some problem space . Tackle problems in parallel to enable the ‘best performance’ possible . Includes not only parallel computing, but also parallel input/output (I/O) . ‘The measure of speed’ in High Performance Computing matters P1 P2 P3 P4 P5 . Common measure for parallel computers established by TOP500 list . Based on benchmark for ranking the best 500 computers worldwide [6] TOP500 Supercomputing Sites Lecture 3 will give in-depth details on parallelization fundamentals & performance term relationships & theoretical considerations Lecture 1 – High Performance Computing 9/ 50 TOP 500 List (June 2019) power challenge [6] TOP500 Supercomputing Sites EU #1 Lecture 1 – High Performance Computing 10 / 50 LINPACK Benchmarks and Alternatives . TOP500 ranking is based on the LINPACK benchmark [7] LINPACK Benchmark implementation . LINPACK solves a dense system of linear equations of unspecified size . LINPACK covers only a single architectural aspect (‘critics exist’) . Measures ‘peak performance’: All involved ‘supercomputer elements’ operate on maximum performance . Available through a wide variety of ‘open source implementations’ . Success via ‘simplicity & ease of use’ thus used for over two decades . Realistic applications benchmark suites might be alternatives . HPC Challenge benchmarks (includes 7 tests) [8] HPC Challenge Benchmark Suite . JUBE benchmark suite (based on real applications) [9] JUBE Benchmark Suite Lecture 1 – High Performance Computing 11 / 50 Multi-core CPU Processors . Significant advances in CPU (or microprocessor chips) . Multi-core architecture with dual, quad, six, or n processing cores . Processing cores are all on one chip one chip . Multi-core CPU chip architecture . Hierarchy of caches (on/off chip) . L1 cache is private to each core; on-chip . L2 cache is shared; on-chip [10] Distributed & Cloud Computing Book . L3 cache or Dynamic random access memory (DRAM); off-chip . Clock-rate for single processors increased from 10 MHz (Intel 286) to 4 GHz (Pentium 4) in 30 years . Clock rate increase with higher 5 GHz unfortunately reached a limit due to power limitations / heat . Multi-core CPU chips have quad, six, or n processing cores on one chip and use cache hierarchies Lecture 1 – High Performance Computing 12 / 50 Dominant Architectures of HPC Systems . Traditionally two dominant types of architectures . Shared-memory parallelization with OpenMP . Distributed-memory parallel programming with the Shared-Memory Computers Message Passing Interface (MPI) standard . Distributed Memory Computers . Often hierarchical (hybrid) systems of both in practice . Dominance in the last couple of years in the community on X86-based commodity clusters running the Linux OS on Intel/AMD processors . More recently, also accelerators play a significant role (e.g., many-core chips) . More recently . Both above considered as ‘programming models’ . Emerging computing models getting relevant for HPC: e.g., quantum devices, neuromorphic devices Lecture 1 – High Performance Computing 13 / 50 Shared-Memory Computers . A shared-memory parallel computer is a system in which a number of CPUs work on a common, shared physical address space [5] Introduction to High Performance Computing for Scientists and Engineers . Two varieties of shared-memory systems: 1. Unified Memory Access (UMA) 2. Cache-coherent Nonuniform Memory Access (ccNUMA) . The Problem of ‘Cache Coherence’ (in UMA/ccNUMA) . Different CPUs use Cache to ‘modify same cache values’ . Consistency between cached data & T1 T2 T3 T4 T5 Memory Shared data in memory must be guaranteed . ‘Cache coherence protocols’ ensure a consistent view of memory Lecture 1 – High Performance Computing 14 / 50 Shared-Memory with UMA . UMA systems use ‘flat memory model’: Latencies and bandwidth are the same for all processors and all memory locations. Also called Symmetric Multiprocessing (SMP) [5] Introduction to High Performance Computing for Scientists and Engineers . Selected Features . Socket is a physical package (with multiple cores), typically a replacable component . Two dual core chips (2 core/socket) . P = Processor core . L1D = Level 1 Cache – Data (fastest) . L2 = Level 2 Cache (fast) . Memory = main memory (slow) . Chipset = enforces cache coherence and mediates connections to memory Lecture 1 – High Performance Computing 15 / 50 Shared-Memory with ccNUMA . ccNUMA systems share logically memory that is physically distributed (similar like distributed-memory systems) . Network logic makes the aggregated memory appear as one single address space [5] Introduction to High Performance Computing for Scientists and Engineers .
Load more

Recommended publications
  • Examining the Viability of FPGA Supercomputing
    1 Examining the Viability of FPGA Supercomputing Stephen D. Craven and Peter Athanas Bradley Department of Electrical and Computer Engineering Virginia Polytechnic Institute and State University Blacksburg, VA 24061 USA email: {scraven,athanas}@vt.edu Abstract—For certain applications, custom computational hardware created using field programmable gate arrays (FPGAs) produces significant performance improvements over processors, leading some in academia and industry to call for the inclusion of FPGAs in supercomputing clusters. This paper presents a comparative analysis of FPGAs and traditional processors, focusing on floating- point performance and procurement costs, revealing economic hurdles in the adoption of FPGAs for general High-Performance Computing (HPC). Index Terms— computational accelerator, digital arithmetic, Field programmable gate arrays, high- performance computing, supercomputers. I. INTRODUCTION Supercomputers have experienced a recent resurgence, fueled by government research dollars and the development of low-cost supercomputing clusters. Unlike the Massively Parallel Processor (MPP) designs found in Cray and CDC machines of the 70s and 80s, featuring proprietary processor architectures, many modern supercomputing clusters are constructed from commodity PC processors, significantly reducing procurement costs. In an effort to improve performance, several companies offer machines that place one or more FPGAs in each node of the cluster. Configurable logic devices, of which FPGAs are one example, permit the device’s hardware to be programmed multiple times after manufacture. A wide body of research over two decades has repeatedly demonstrated significant performance improvements for certain classes of applications when implemented within an FPGA’s configurable logic [1]. Applications well suited to speed-up by FPGAs typically exhibit massive parallelism and small integer or fixed-point data types.
    [Show full text]
  • Overview of the SPEC Benchmarks
    9 Overview of the SPEC Benchmarks Kaivalya M. Dixit IBM Corporation “The reputation of current benchmarketing claims regarding system performance is on par with the promises made by politicians during elections.” Standard Performance Evaluation Corporation (SPEC) was founded in October, 1988, by Apollo, Hewlett-Packard,MIPS Computer Systems and SUN Microsystems in cooperation with E. E. Times. SPEC is a nonprofit consortium of 22 major computer vendors whose common goals are “to provide the industry with a realistic yardstick to measure the performance of advanced computer systems” and to educate consumers about the performance of vendors’ products. SPEC creates, maintains, distributes, and endorses a standardized set of application-oriented programs to be used as benchmarks. 489 490 CHAPTER 9 Overview of the SPEC Benchmarks 9.1 Historical Perspective Traditional benchmarks have failed to characterize the system performance of modern computer systems. Some of those benchmarks measure component-level performance, and some of the measurements are routinely published as system performance. Historically, vendors have characterized the performances of their systems in a variety of confusing metrics. In part, the confusion is due to a lack of credible performance information, agreement, and leadership among competing vendors. Many vendors characterize system performance in millions of instructions per second (MIPS) and millions of floating-point operations per second (MFLOPS). All instructions, however, are not equal. Since CISC machine instructions usually accomplish a lot more than those of RISC machines, comparing the instructions of a CISC machine and a RISC machine is similar to comparing Latin and Greek. 9.1.1 Simple CPU Benchmarks Truth in benchmarking is an oxymoron because vendors use benchmarks for marketing purposes.
    [Show full text]
  • Performance of a Computer (Chapter 4) Vishwani D
    ELEC 5200-001/6200-001 Computer Architecture and Design Fall 2013 Performance of a Computer (Chapter 4) Vishwani D. Agrawal & Victor P. Nelson epartment of Electrical and Computer Engineering Auburn University, Auburn, AL 36849 ELEC 5200-001/6200-001 Performance Fall 2013 . Lecture 1 What is Performance? Response time: the time between the start and completion of a task. Throughput: the total amount of work done in a given time. Some performance measures: MIPS (million instructions per second). MFLOPS (million floating point operations per second), also GFLOPS, TFLOPS (1012), etc. SPEC (System Performance Evaluation Corporation) benchmarks. LINPACK benchmarks, floating point computing, used for supercomputers. Synthetic benchmarks. ELEC 5200-001/6200-001 Performance Fall 2013 . Lecture 2 Small and Large Numbers Small Large 10-3 milli m 103 kilo k 10-6 micro μ 106 mega M 10-9 nano n 109 giga G 10-12 pico p 1012 tera T 10-15 femto f 1015 peta P 10-18 atto 1018 exa 10-21 zepto 1021 zetta 10-24 yocto 1024 yotta ELEC 5200-001/6200-001 Performance Fall 2013 . Lecture 3 Computer Memory Size Number bits bytes 210 1,024 K Kb KB 220 1,048,576 M Mb MB 230 1,073,741,824 G Gb GB 240 1,099,511,627,776 T Tb TB ELEC 5200-001/6200-001 Performance Fall 2013 . Lecture 4 Units for Measuring Performance Time in seconds (s), microseconds (μs), nanoseconds (ns), or picoseconds (ps). Clock cycle Period of the hardware clock Example: one clock cycle means 1 nanosecond for a 1GHz clock frequency (or 1GHz clock rate) CPU time = (CPU clock cycles)/(clock rate) Cycles per instruction (CPI): average number of clock cycles used to execute a computer instruction.
    [Show full text]
  • Investigations of Various HPC Benchmarks to Determine Supercomputer Performance Efficiency and Balance
    Investigations of Various HPC Benchmarks to Determine Supercomputer Performance Efficiency and Balance Wilson Lisan August 24, 2018 MSc in High Performance Computing The University of Edinburgh Year of Presentation: 2018 Abstract This dissertation project is based on participation in the Student Cluster Competition (SCC) at the International Supercomputing Conference (ISC) 2018 in Frankfurt, Germany as part of a four-member Team EPCC from The University of Edinburgh. There are two main projects which are the team-based project and a personal project. The team-based project focuses on the optimisations and tweaks of the HPL, HPCG, and HPCC benchmarks to meet the competition requirements. At the competition, Team EPCC suffered with hardware issues that shaped the cluster into an asymmetrical system with mixed hardware. Unthinkable and extreme methods were carried out to tune the performance and successfully drove the cluster back to its ideal performance. The personal project focuses on testing the SCC benchmarks to evaluate the performance efficiency and system balance at several HPC systems. HPCG fraction of peak over HPL ratio was used to determine the system performance efficiency from its peak and actual performance. It was analysed through HPCC benchmark that the fraction of peak ratio could determine the memory and network balance over the processor or GPU raw performance as well as the possibility of the memory or network bottleneck part. Contents Chapter 1 Introduction ..............................................................................................
    [Show full text]
  • Intel® Math Kernel Library (Intel® MKL) 10.2 In-Depth Intel® Math Kernel Library (Intel® MKL) 10.2: In-Depth
    Intel® Math Kernel Library (Intel® MKL) 10.2 In-Depth Intel® Math Kernel Library (Intel® MKL) 10.2: In-Depth Contents Intel® Math Kernel Library (Intel® MKL) 10.2. .4 Performance Improvements in Intel MKL 10.2. 6 Highlights . 4 Performance Improvements in Intel MKL 10.1. 7 Features. 4 Performance Improvements in Version 10.0. 7 Multicore ready . 4 BLAS . 7 Automatic runtime processor detection . .4 LAPACK . 7 Support for C and Fortran interfaces . 4 FFTs . 7 Support for all Intel® processors in one package . 4 VML/VSL . .7 Royalty-free distribution rights . 4 Functionality. 7 New in Intel MKL 10.2. 4 Linear Algebra: BLAS and LAPACK . .7 Performance Improvements . 4 BLAS . 8 C#/ .Net support . 4 Sparse BLAS . 8 BLAS . 4 LAPACK . .8 LAPACK . .5 BLAS and LAPACK Performance . .8 FFT . 5 Linear Algebra: ScaLAPACK . 9 PARDISO . 5 ScaLAPACK Performance . 9 New in Intel® MKL 10.1. .5 Raw Performance . 9 Computational Layer . .5 Block Size Robustness . 10 PARDISO Direct Sparse Solver . 5 References. 10 Sparse BLAS . .5 Linear Algebra: Sparse Solvers . 1. 0 LAPACK . 5 PARDISO*: Parallel Direct Sparse Solver . 11 Discrete Fourier Transform Interface (DFTI) . 5 New Out-of-Core Support! . 1. 1 Iterative Solver Preconditioner . 6 Iterative Solvers . .11 Vector Math Functions . 6 FGMRES Solver . 1. 1 User’s Guide . 6 Conjugate Gradient Solver . 11 ILU0/ILUT Preconditioners . 1. 2 Sparse BLAS . 1. 2 2 Intel® Math Kernel Library (Intel® MKL) 10.2: In-Depth References. 12 LINPACK Benchmark . 19 Fast Fourier Transforms (FFT) . 1. 2 Ease of Use . 19 Interfaces . .12 Performance . 20 Fortran and C .
    [Show full text]
  • PT-365-Updated-Classroom-Material-March-May-20.Pdf
    Dear Students, Hope your preparation is going well. We wish to communicate our plan, at part of PT 365, for the upcoming prelims examination. Given that Prelims examination is now scheduled for 4th October, we will be covering current affairs till the month of August in the following manner - • PT 365 Updation - o Coverage - Current affairs for the months of March, April and May • PT 365 Extended - o Tentative date of release - 10th September o Coverage - Current affairs for the months of June, July and August Hope these documents help you in boosting your preparation and building up your confidence further as you wind up your preparations. Best Wishes Team Vision IAS Table of Contents 1. POLITY AND CONSTITUTION __________ 4 2.2.2. Organisation for the Prohibition of Chemical 1.1. Issues Related to Constitution ________ 4 Weapons _____________________________ 15 1.1.1. Right to Property____________________ 4 2.2.3. Multilateral Development Banks ______ 15 1.1.2. Reservation in Scheduled Areas ________ 4 2.2.4. WHO ____________________________ 16 1.1.3. Jammu & Kashmir Domicile Rules_______ 5 2.2.4.1. World Health Assembly (WHA) ____ 16 1.1.4. Constitutional Articles in News _________ 5 2.2.4.2. WHO executive board ___________ 16 1.2. Issues Related to Functioning of 2.2.4.3. World Health Organization Funding 16 Parliament/ State Legislature/Local 2.3. International Events _______________ 17 2.3.1. UN75 ___________________________ 17 Government __________________________ 6 2.3.2. Open Skies Treaty __________________ 17 1.2.1. Rajya Sabha Elections ________________ 6 2.3.3.
    [Show full text]
  • Supercomputers – Prestige Objects Or Crucial Tools for Science and Industry?
    Supercomputers – Prestige Objects or Crucial Tools for Science and Industry? Hans W. Meuer a 1, Horst Gietl b 2 a University of Mannheim & Prometeus GmbH, 68131 Mannheim, Germany; b Prometeus GmbH, 81245 Munich, Germany; This paper is the revised and extended version of the Lorraine King Memorial Lecture Hans Werner Meuer was invited by Lord Laird of Artigarvan to give at the House of Lords, London, on April 18, 2012. Keywords: TOP500, High Performance Computing, HPC, Supercomputing, HPC Technology, Supercomputer Market, Supercomputer Architecture, Supercomputer Applications, Supercomputer Technology, Supercomputer Performance, Supercomputer Future. 1 e-mail: [email protected] 2 e-mail: [email protected] 1 Content 1 Introduction ..................................................................................................................................... 3 2 The TOP500 Supercomputer Project ............................................................................................... 3 2.1 The LINPACK Benchmark ......................................................................................................... 4 2.2 TOP500 Authors ...................................................................................................................... 4 2.3 The 39th TOP500 List since 1993 .............................................................................................. 5 2.4 The 39th TOP10 List since 1993 ...............................................................................................
    [Show full text]
  • Understanding IBM Pseries Performance and Sizing
    Understanding IBM pSeries Performance and Sizing Comprehend IBM RS/6000 and IBM ^ pSeries hardware architectures Get an overview of current industry benchmarks Understand how to size your system Nigel Trickett Tatsuhiko Nakagawa Ravi Mani Diana Gfroerer ibm.com/redbooks SG24-4810-01 International Technical Support Organization Understanding IBM ^ pSeries Performance and Sizing February 2001 Take Note! Before using this information and the product it supports, be sure to read the general information in Appendix A, “Special notices” on page 377. Second Edition (February 2001) This edition applies to IBM RS/6000 and IBM ^ pSeries as of December 2000, and Version 4.3.3 of the AIX operating system. This document was updated on January 24, 2003. Comments may be addressed to: IBM Corporation, International Technical Support Organization Dept. JN9B Building 003 Internal Zip 2834 11400 Burnet Road Austin, Texas 78758-3493 When you send information to IBM, you grant IBM a non-exclusive right to use or distribute the information in any way it believes appropriate without incurring any obligation to you. © Copyright International Business Machines Corporation 1997, 2001. All rights reserved. Note to U.S Government Users – Documentation related to restricted rights – Use, duplication or disclosure is subject to restrictions set forth in GSA ADP Schedule Contract with IBM Corp. Contents Preface. 9 The team that wrote this redbook. 9 Comments welcome. 11 Chapter 1. Introduction . 1 Chapter 2. Background . 5 2.1 Performance of processors . 5 2.2 Hardware architectures . 6 2.2.1 RISC/CISC concepts . 6 2.2.2 Superscalar architecture: pipeline and parallelism . 7 2.2.3 Memory management .
    [Show full text]
  • AMD Opteron™ Processor Benchmarking for Clustered Systems
    W H I T E P A P E R AMD Opteron™ Processor Benchmarking for Clustered Systems Doug O’flaherty and Michael Goddard AMD One AMD Place Sunnyvale, CA 94088 Page 1 AMD Opteron™ Processor Benchmarking for Clustered Systems July 15, 2003 W H I T E P A P E R Objective The selection of a High-Performance Computing (HPC) platform is a process of evaluation and analysis. The goal is to deliver the appropriate combination of SMP and cluster configuration, processor, memory, interconnect, and storage that optimizes performance. This is often done without being able to run the customer-specific application on the complete system prior to selection. Since the application specific metrics are absent, industry benchmarks provide a basis for comparison. Industry standard benchmarks are system or sub-system metrics for performing a particular computing task. There are as many benchmarks as there are computing tasks. This paper examines AMD Opteron™ processor performance across a suite of industry standard benchmarks. The metrics reflect the AMD Opteron processor’s unique architecture, which balances bandwidth with outstanding computing performance to deliver true scalability for HPC applications. Introduction Benchmarks seek to provide comparative results—a quantitative analysis of disparate systems performing similar computational tasks. The benchmarking effort typically attempts to set performance expectations of real world tasks. However, to achieve objective results, each benchmark is limited in the scope of its measurements. Some benchmarks emphasize raw floating-point operations per second, while others measure memory access latency and bandwidth, while others script a particular workload in a specific application. Because applications are diverse and more complex than a combination of metrics, no single benchmark is a metric of a processor’s ability to perform real-world computation.
    [Show full text]
  • Solution of Algebraic Equations by Using Autonomous Computational Methods
    Solution of Algebraic Equations by Using Autonomous Computational Methods Andrew Pownuk Department of Mathematical Sciences University of Texas at El Paso, El Paso, Texas, USA [email protected], https://andrew.pownuk.com AMS Fall Central Sectional Meeting September 12-13, 2020 1 / 63 Outline 1 Game Theory 2 Autonomous Computational Methods 3 Algebraic Equations 4 Generalizations and Possible Limitations 5 Autonomous Computational Methods 6 Machine Learning 7 Conclusions 2 / 63 Checkers (Game Theory) Game Theory Autonomous Computational Methods Algebraic Equations Generalizations and Possible Limitations Autonomous Computational Methods Machine Figure: Game tree Learning Conclusions Arthur Samuel in 1959 applied alphabeta pruning in order to create a program that learned how to play checkers. Alphabeta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. 3 / 63 Game Theory ( tic-tac-toe) Game Theory Autonomous Computational Methods Algebraic Equations Generalizations and Possible Limitations Autonomous Computational Methods Machine Learning Conclusions Figure: Game tree 4 / 63 Game Theory (GO) Game Theory Autonomous Computational Methods Algebraic Equations Generalizations and Possible Limitations Autonomous Computational Methods Machine Learning Conclusions Figure: Game tree 5 / 63 Game Theory (Winning Strategy) Game Theory Autonomous Computational Methods Algebraic Equations Generalizations and Possible Limitations Autonomous Computational Methods Machine Learning Conclusions Figure: Game tree 6 / 63 Basic Mathematical Operations Game Theory Autonomous Computational Addition Methods 1 + 1 = 2 Algebraic Equations 1 + 0 = 1 Generalizations and Possible Limitations 2 + (−1) = 1 Autonomous Computational Multiplication Methods 1 ∗ 0 = 0 Machine Learning i ∗ i = −1 Conclusions Algebra a + b = b + a a(b + c) = ab + ac etc.
    [Show full text]
  • 12121Ijwest01.Pdf
    International Journal of Web & Semantic Technology (IJWesT) Vol.12, No.1, January 2021 U-MENTALISM PATENT: THE BEGINNING OF CINEMATIC SUPERCOMPUTATION Luís Homem Centro de Filosofia das Ciências da Universidade de Lisboa ABSTRACT This paper discloses in synthesis a super-computation computer architecture (CA) model, presently a provisional Patent Application at INPI (nº 116408). The outline is focused on a method to perform computation at or near the speed of light, resorting to an inversion of the Princeton CA. It expands from isomorphic binary/RGB (typical) digital “images”, in a network of (UTM)s over Turing-machines (M)s. From the binary/RGB code, an arithmetic theory of (typical) digital images permits fully synchronous/orthogonal calculus in parallelism, wherefrom an exponential surplus is achieved. One such architecture depends on any “cell”-like exponential-prone basis such as the “pixel”, or rather the RGB “octet-byte”, limited as it may be, once it is congruent with any wave-particle duality principle in observable objects under the electromagnetic spectrum and reprogrammable designed. Well-ordered instructions in binary/RGB modules are, further, programming composed to alter the structure of the Internet, in virtual/virtuous eternal recursion/recurrence, under man-machine/machine-machine communication ontology. KEYWORDS U-Mentalism, Super-computation, Computer Architecture, Cybernetics, Programming Languages Design 1. INTRODUCTION This document is intended to serve as white paper to describe in the most possible composed details
    [Show full text]
  • Hardware Architecture and Basics of Parallel Computing
    Hardware architecture and basics of parallel computing Gian Franco Marras [email protected] Dipartimento Supercalcolo, Applicazioni e Innovazione (SCAI) CINECA - High Performance System Group Casalecchio di Reno (BO) – Italy www.cineca.it - www.cineca.it/en/index.htm Outline • Parallel Architectures & Parallel Programming • Message Passing Interface • Point-point comunication • Collective comunication • OpenMP • Directives • Runtime Library Routines • Environment Variables Parallel Architectures and Parallel Programming An overview What is a Supercomputer? A supercomputer is a computer that is at the frontline of current processing capacity, particulary speed of calculation. Supercomputers are used for highly calculation- intensive tasks such as problems involving quantum physics, weather forecasting, climate research, molecular modeling, physical simulations and a particular class of problems, known as Grand Challenge problems. What is Grand Challenge Problem? A grand challenge is a fundamental problem in science or engineering, with broad applications, whose solution would be enabled by the application of high performance computing resources that could become available in the near future. Which are Grand Challenges today? • Prediction of weather and global change • Material science and Superconductivity • Structural biology • Human genome • Astronomy • Turbolence • Design of hypersonic aircraft • Geophysics • ... Parallel computing Parallel computing is a form of computation in which many calculations are carried out simultaneously,
    [Show full text]